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sukhopar [10]
2 years ago
13

Find the value of x. Give reasons to justify your solution. b ∈ ac, d ∈ fa

Mathematics
1 answer:
tatiyna2 years ago
6 0

Answer:

x = 27

Step-by-step explanation:

∠ ABD and ∠ BDE are alternate angles and are congruent, then

∠ BDE = 72°

∠ ADB + ∠ BDE + ∠ EDF = 180° ( sum of angles on a straight line ), that is

2x + 72 + 2x = 180

4x + 72 = 180 ( subtract 72 from both sides )

4x = 108 ( divide both sides by 4 )

x = 27

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miss Akunina [59]
150g/12cakes
150/12 = 12.5
12.5g/cake
12.5x30 = 375
Therefore, you need 375g for 30 cakes.
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3 years ago
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1.Find the dot product of the two given vectors, u=(1,6) and v=(-5,-2) 2. Find the dot product of v=-7i+4j and w=-6i+5j
Svet_ta [14]
The dot product of the two vectors will be given as follows:
v*w=(-7i+4j)*(-6i+5j)
=(-7*(-6))i+(4*5)j
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Hence the answer is:
v*w=(-42i+20j)
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3 years ago
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Stan earns $12 per hour by working as an intern at a law firm. How much money does he earn in a week in which he works 28 hours?
torisob [31]

Answer:

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Step-by-step explanation:

Stan works for 28 hours and gets paid $12 for each hour, so the amount of money he gets in total is $12*28 = $336.

8 0
2 years ago
Need help on these !! 13 and 14! Please!!
katen-ka-za [31]

Question # 13

Answer:

The required equation for the given function is <em>y = 4sin(x/2+2π/3) -2 , as shown attached graph diagram.</em>

<em>Step-by-step explanation: </em>

As the general sine function is given by

y=asin(bx+c)+d.......[A]

  • amplitude = a
  • period = 2π ÷ b
  • Phase shift = -c ÷ b
  • Vertical shift = d

As in the question,  

  • amplitude = a = 4
  • period = 4π
  • phase shift = -4π/3
  • Vertical shift = d = -2

As  

period = 2π ÷ b  

b = 2π/period

b = 2π/4π ∵ period = 4π

b = 1/2  

Also

Phase shift = -c/b

-4π/3 = -c/b ∵ phase shift = -4π/3

4π/3 = c/b  

c = b × 4π/3  

c = 1/2 × 4π/3  

c = 4π/6  

c = 2π/3

So, putting Amplitude ⇒ a = 4, Vertical shift ⇒ d = -2, b = 1/2 ,  

and c = 2π/3 in Equation [A] would bring us the required equation for the given function.

y=asin(bx+c)+d

y = 4sin(x/2+2π/3)+(-2)

y = 4sin(x/2+2π/3) -2            

<em>Note: The graph is also shown in attached diagram.</em>

                                             Question # 14

<em>Answer:</em>

The required equation for the given function is y = cot(x+π/3)+2, as shown in attached graph diagram.

<em>Step-by-step explanation: </em>

As the general cotangent function is given by

y=acot(bx+c)+d.......[A]

  • amplitude = a
  • period = π ÷ b
  • Phase shift = -c ÷ b
  • Vertical shift = d

As in the question,  

  • period = π
  • phase shift = -π/3
  • Vertical shift = d = 2

As  

period = π ÷ b  

b = π/period

b = π/π ∵ period = 4π

b = 1  

Also

Phase shift = -c/b

-π/3 = -c/b ∵ phase shift = -π/3

π/3 = c/b  

c = b × π/3  

c = 1 × π/3  

c = π/3

So, putting vertical shift ⇒ d = 2, b = 1 and   c = π/3 in Equation [A] would bring us the required equation for the given function.

y=acot(bx+c)+d

y = cot(x+π/3)+2

<em>Note: The graph is also shown in attached diagram.</em>

Keywords: amplitude, period , phase shift , vertical shift

Learn more about trigonometric functions of equations from brainly.com/question/2643311

#learnwithBrainly

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Zepler [3.9K]

Answer:

17>n is the correct answer

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